A teepee made by a tweaker, usually out of old cardboard and electrical wires from appliances they have taken apart and forgotten how to put back together.

"Yo, you see that tweaker makin' a teepee over on skid row this morning?"
"No, but I did see a tweaker making a tweepee."

OR

"Hey what happened to your roomate? He doesn't live in the house anymore?"
"Naa man that tweaker spent all his money on dope, now he pays me $20 a month to live in that tweepee he made in the backyard."